The BW overdrive has the shafting that goes straight through but does have the larger diameter shafting due to the planetary set and the freewheeling drum. I think they used the smaller R10 housing for most conversions so they are relatively short. I think Studebaker, Nash, and Willys used those. The Ford ones are a bit longer in the tail. The solenoid and governor are there but don't add a lot of weight. All the R10s have the same basic step in ratio.
The Mitchel has the aluminum case but it is larger and fairly robust to be able to support the two shaft system. It has a main shaft and counter shaft much like regular manual transmission. There is an input gear shaft and an output gear shaft with the synchroniser between the two. The cluster gear runs on the counter shaft. The unit has a fairly heavy duty shift fork assembly to effect the gear change.
If one is heavier than the other then it wouldn't be by much.
The OP mentions that his BW overdrive is sometimes forced out of direct drive during deceleration due to wear in the lock out mechanism. While I've not operated the model A conversions, I do have a lot of miles on both my Mercury cars. I've never experience a drop out of lockout. The way the lever engages the lock out rod, it remains in place pretty well even though the control rod is spring loaded. There must be some pretty heavy wear in either the rod or the end of the lever in there. The one warning than is in the 1949 through 1951 Lincoln-Mercury Overhaul Manual is that the car should not be operated in 2nd and overdrive for too long. I guess it makes the planetary spin too fast under sustained use. There is nothing in the troubleshooting info about problems with direct drive. When we used to take our original family car on trips to Colorado, coming down those mountain passes required a lot of use in direct drive. It was actually more common to have the overdrive unit lock up when it failed. I've know two people that have had high speed lock up and it scared the hell out of them. Needless to say, their planetary unit was shredded.
Since the model A conversion doesn't have the reverse lockout mechanism, it must be getting more wear due to constant cable pull operation in order to reverse the car. That action doesn't affect the cable pull in an overdrive transmission car since all the lockout action comes from the shift mechanism in the transmission section.